利用FDTD与传输方程混合计算散射系数的方法

利用FDTD(F in ite-D ifference Tim e-Domain)方法分析天线等无耗传输线馈电问题的散射系数时,为了得到输入电压和反射电压的时域信号,必须将FDTD仿真程序重复运行两遍.这对计算域较大的问题来说要花费很长的仿真时间和占用较大的存储容量,而实际散射系数中用到的端口输入电压与激励信号在时域波形上必须完全一致,只不过因为输入端口取样位置的不同,输入电压相对于激励信号在时间上有所延迟.对于无耗传输线其反射电压的最大值与输入电压的最大值应该相等.因此,利用已知的输入电压取样位置和电磁波的传输速度,并结合无耗传输线的波动方程(电报方程),可以从理论上推导出输入电压的时域波形和表示方程.这样在计算散射参数时就不需要用FDTD仿真来获得输入信号,而只需要进行一次FDTD运算获得所需的反射信号即可.在此不仅推导出了无耗传输线上任意一点电压、电流的时域表达式,还利用它计算出了微带线馈电的矩形贴片天线和低通滤波器的散射参数,并与二次FDTD仿真获得的结果进行了对比,二者结果完全一致.但使用此方法使仿真时间和存储量都节约了一倍.

A Method to Calculate Scattering Parameters in Combination with FDTD Simulation and Transmission Equation

The FDTD simulation procedure must be run twice when it is used to calculate the scattering parameters of the antenna and other objects fed with the lossless transmission line in order to obtain the time domain input voltage and output voltage distribution.Therefore,the larger the FDTD computational domain is,the larger the simulation time and storage space is required. However,the input voltage distribution is only the voltage excitation source delayed in time.On the lossless transmission line,the reflection voltage is equal to the input voltage in the amplitude,so a formulation and the distribution of the input voltage in time domain can be found in theory by using the distance from the observe point to the excitation source,electromagnetic field propagating speed and the transmission equation(or telegraph equation).The FDTD simulation program needn't been run to obtain the input voltage when the scattering parameters are calculated.In this method,the FDTD program is only run once to obtain the reflection voltage distribution in time.This paper not only gives out the time domain equation of the input voltage and current on a point of the lossless transmission line,but also calculates the scattering parameters of a patch antenna and a low-pass filter with the method.The numerical experiments have shown that the method in this paper is in good agreement with that from the twice' s FDTD simulation.The storage space and the simulation time are all reduced even to a half as usual.